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Derive the heat equation for a homogeneous one-dimensional rod with a non-constant crosssection of area A(x)...

Derive the heat equation for a homogeneous one-dimensional rod with a non-constant crosssection of area A(x) and perimeter P(x). Suppose that the lateral surface is not insulated and the amount of heat energy leaving the rod via the lateral surface per unit area per unit time is proportional to the difference of the temperature in the rod and the temperature w(x, t) of the air surrounding the rod (use the coefficient of proportionality α). Furthermore, suppose that there are no heat sources.

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The solution is as follows

genius_generous answered 1 year ago
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